Question 769654
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The other tutor used 1 unknown.  Here it is using 2. Word problems involving
multiply answers are usually easier to set up if you use multiple unknowns.

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: 1 jar contains 5/6 alcohol and another 8/9 alcohol . how many liters taken from each jar are required to fill a third jar with capacity of 24 liter so that the mixture will be seven eighths.
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Let the answer be

We take x liters out of the first jar and y liters out of the second jar,
so that x + y = 24 liters.

The amount of alcohol in the x liters is {{{5/6}}}x [and the rest water].

The amount of alcohol in the y liters is {{{8/9}}}y [and the rest water].

So the amount of alcohol in the third jar is {{{5/6}}}x + {{{8/9}}}y [and the
rest water].

The third jar contains 24 liters.

So also the amount of alcohol in the third jar is {{{7/8}}}·24 or 21 liters of
alcohol [and the rest water].

So we set the two expressions for the amount of alcohol in the third jar
equal, and we have

               {{{5/6}}}x + {{{8/9}}}y  = 21

So our system of equations is

               {{{5/6}}}x + {{{8/9}}}y  = 21
                          x + y = 24

Clear the first of fractions by multiplying it through by LCD of 18

               15x + 16y = 21
                   x + y = 24

Solve that system and get x = 6 and y = 18

Answer: Take 6 liters from the jar that contains {{{5/6}}}ths alcohol and 
18 liters from the jar that contains {{{8/9}}}ths alcohol.

Edwin</pre>